This study provides a statistical study of train delay data in the Swedish railway system. We assess the goodness of fit of common distributions---such as gamma, log-normal, and inverse Gaussian---to model train arrival times and identify delay patterns for each station and travel direction. The Kolmogorov-Smirnov (K-S) statistical test was applied to determine the best-fitting distributions for arrival times at ten stations. Preliminary findings indicate distinct behaviors across stations, with the log-normal distribution fitting 70% of stations. However, unique patterns, such as direction-specific delays, were observed in certain stations, highlighting the importance of localized analysis. Traditionally, in Sweden, train delays have been treated as uniformly distributed across the network, a simplification widely adopted in developing synthetic datasets for AI-based timetable rescheduling systems. This study disproves the uniformity assumption, demonstrating significant variability across locations and directions. By emphasizing the need for station- and direction-specific modeling, we provide key insights that contribute to creating more accurate synthetic datasets for AI-driven timetable rescheduling. These findings promote the development of data-driven systems that improve predictive modeling, operational efficiency, and overall reliability in railway networks.